Backward inducing and exponential decay of correlations for partially hyperbolic attractors

Wasserstein convergence rates in the invariance principle for deterministic dynamical systems

“…Hence, for all , . Specific examples are: some partially hyperbolic systems with a mostly contracting direction [7, 12]; unimodal maps and multimodal maps as in [20] for a fixed system; and Hénon-type attractors [19]. Let be defined by for , , where b is small enough depending on a .…”

Exponential decay of random correlations for random Anosov systems mixing on fibers

“…Liverani in [28] used it to prove the exponential decay of correlations for smooth uniformly hyperbolic area-preserving cases. Later, it was generalized to general Axiom A attractors in [35,5], and some partially hyperbolic systems [2,12]. For RDS, the Birkhoff cone approach was used in [7] and [34] (we mentioned before) for exponential decay of (quenched) random correlations.…”

Shadowing by non-uniformly hyperbolic periodic points and uniform hyperbolicity

“…Let g : M → M be a diffeomorphism on a compact manifold M. We say that an invariant set S ⊂ M is a NUH set or, simply, NUH, iff (1) there is an Dg-invariant splitting T S M = E cs ⊕ E cu , (2) there exists η < 0 and an adapted Riemannian metric for which any point p ∈ S satisfies lim inf…”

“…Analogously, we define a cone over E u (p) of width a. Now we adapt the definition of hyperbolic times to the context of diffeomorphisms (see also [1]).…”